Analytic determination of the transient response of a thin-wire antenna based upon an SEM representation

Based upon an analytical expression for the frequency-domain current induced on a thin-wire antenna, a theory for determining the singular expansion method (SEM) representation of the transient response of an unloaded transmitting as well as a receiving antenna is presented. An analytical expression for the SEM poles is derived, and the explicit expressions for the associated coefficients, natural mode current, and coupling coefficient, are uncovered. A theoretical explanation for some of the physical processes related to the SEM representation of the transient current on a thin-wire antenna is also provided. Excellent agreement with the numerical results for both the transmitting and receiving antennas is obtained.